fix(windows): broken PATH propagation, ps usage, and claude binary resolution

- sherpa-runtime-env: use case-insensitive key lookup when modifying PATH
  on plain env objects. On Windows, `{...process.env}` stores PATH as
  `Path` but `applySherpaLoaderEnv` used hardcoded `"PATH"`, creating a
  duplicate key that could shadow the real system PATH in child processes.

- runtime-toolchain: use `wmic` on Windows instead of Unix-only `ps -o`
  to resolve the node executable path from a PID.

- claude-agent: pass `findExecutable("claude")` as
  `pathToClaudeCodeExecutable` so the SDK uses the user's installed
  binary when available. Update spawn hook to only replace bare
  "node"/"bun" with process.execPath, preserving native binary paths.

- desktop/paseo.cmd: use ELECTRON_RUN_AS_NODE with node-entrypoint-runner
  for the Windows CLI wrapper.

packages/cli/src/commands/daemon/runtime-toolchain.ts

@@ -1,4 +1,5 @@
 import { spawnSync } from "node:child_process";
+import { platform } from "node:os";
 
 export interface NodePathFromPidResult {
   nodePath: string | null;
@@ -12,17 +13,14 @@ function normalizeError(error: unknown): string {
   return String(error);
 }
 
-export function resolveNodePathFromPid(pid: number): NodePathFromPidResult {
+function resolveNodePathFromPidUnix(pid: number): NodePathFromPidResult {
   const result = spawnSync("ps", ["-o", "comm=", "-p", String(pid)], {
     encoding: "utf8",
     stdio: ["ignore", "pipe", "pipe"],
   });
 
   if (result.error) {
-    return {
-      nodePath: null,
-      error: `ps failed: ${normalizeError(result.error)}`,
-    };
+    return { nodePath: null, error: `ps failed: ${normalizeError(result.error)}` };
   }
 
   if ((result.status ?? 1) !== 0) {
@@ -34,12 +32,36 @@ export function resolveNodePathFromPid(pid: number): NodePathFromPidResult {
   }
 
   const resolved = result.stdout.trim();
-  if (!resolved) {
+  return resolved ? { nodePath: resolved } : { nodePath: null, error: "ps returned an empty command path" };
+}
+
+function resolveNodePathFromPidWindows(pid: number): NodePathFromPidResult {
+  const result = spawnSync(
+    "wmic",
+    ["process", "where", `ProcessId=${pid}`, "get", "ExecutablePath", "/VALUE"],
+    { encoding: "utf8", stdio: ["ignore", "pipe", "pipe"] },
+  );
+
+  if (result.error) {
+    return { nodePath: null, error: `wmic failed: ${normalizeError(result.error)}` };
+  }
+
+  if ((result.status ?? 1) !== 0) {
+    const details = result.stderr?.trim();
     return {
       nodePath: null,
-      error: "ps returned an empty command path",
+      error: details ? `wmic failed: ${details}` : `wmic exited with code ${result.status ?? 1}`,
     };
   }
 
-  return { nodePath: resolved };
+  // wmic output format: "ExecutablePath=C:\path\to\node.exe\r\n"
+  const match = result.stdout.match(/ExecutablePath=(.+)/);
+  const resolved = match?.[1]?.trim();
+  return resolved ? { nodePath: resolved } : { nodePath: null, error: "wmic returned no executable path" };
+}
+
+export function resolveNodePathFromPid(pid: number): NodePathFromPidResult {
+  return platform() === "win32"
+    ? resolveNodePathFromPidWindows(pid)
+    : resolveNodePathFromPidUnix(pid);
 }